Abstract

Let B be a Galois algebra with Galois group G, Jg={b∈B|bx=g(x)bfor allx∈B} for each g∈G, and
BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|g∈G}, e a nonzero
element in Ba, and He={g∈G|eeg=e}. Then, a
monomial e is characterized, and the Galois extension Be,
generated by e with Galois group He, is investigated.

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